After many years without such a service, Microsoft is finally allowing users to migrate their Xbox Live accounts to a different country, enabling users who move across country lines to access the services specific to their new country. The request process is not simple, and can take up to 6 weeks to migrate during which you will not be able to use your account.

Also worthy of noting is that there is a significant chance that you will lose access to content you have purchased and downloaded through Xbox Live. Anyone who migrates their account should also be aware that not all the content available in the previous country will be available in the new content, with geofencing affecting some content that is available due to specific Microsoft content licenses.

Here is the full slab of info from the Microsoft Support Forums:

You have chosen to migrate your Xbox LIVE account to a new country. You should be aware that certain Xbox LIVE content, features and functions may vary depending on your location, due to licensing limitations provided by specific providers. In order to proceed, you must confirm that you have been informed of and fully understand the consequences of the migration of your Xbox Live account:

Microsoft reminds you that the migration of your Xbox Live account will have the following consequences:

Some of the services and content that you are currently benefiting from in the country originally registered may not also be available in the country you are willing to migrate to.

All of your current subscriptions, except for Xbox Live Gold if you had any, will be cancelled.
You may lose the ability to re-download some, if not all, of the content in your download history.

Any content that you will subsequently download after the account is migrated will be subject to any applicable geofencing rules of your new location.

Note on Geofencing: If you bought something in the country you originally registered in that wasn't geofenced, it could be that it will be if bought again, in your new location. These geofencing constraints depend on the license to distribute that Microsoft was granted by the content providers.

Please note that the migration process can take up to 6 weeks. During this time your account will not be available. No refunds will be given for any content that is lost during the migration.